Many of today.s most striking buildings are nontraditional freeform shapes. A new
field of mathematics, discrete differential geometry, makes it possible to construct
these complex shapes that begin as designers. digital creations. Since it.s impossible
to fashion a large structure out of a single piece of glass or metal, the design
is realized using smaller pieces that best fit the original smooth surface. Triangles
would appear to be a natural choice to represent a shape, but it turns out that
using quadrilaterals.which would seem to be more difficult.saves material and
money and makes the structure easier to build.

One of the primary goals of researchers is to create an efficient, streamlined
process that integrates design and construction parameters so that early on
architects can assess the feasibility of a given idea. Currently, implementing a
plan involves extensive (and often expensive) interplay on computers between
subdivision.breaking up the entire structure into manageable manufacturable
pieces.and optimization.solving nonlinear equations in high-dimensional spaces
to get as close as possible to the desired shape. Designers and engineers are
seeking new mathematics to improve that process. Thus, in what might be characterized
as a spiral with each field enriching the other, their needs will lead to new
mathematics, which makes the shapes possible in the first place.

For More Information:

.Geometric computing for freeform architecture,.
J. Wallner and H. Pottmann. Journal of Mathematics in Industry, Vol. 1, No. 4, 2011.